Pricing Forward With Continuous Dividend Yield

Forward Price

The predetermined and agreed-upon price of an underlying asset in a forward contract

What is Forward Price?

Forward price refers to the predetermined and agreed upon price of an underlying asset in a forward contract. It is also known as the forward rate.

A forward contract refers to an agreement between parties to buy or sell an underlying asset on an agreed-upon date and price. The underlying asset can be a currency, commodity, or any other financial asset.

The asset is agreed upon by both the purchaser and seller (two parties) entering into the forward contract. Upon the agreement's commencement, the contract is valued at 0 since market conditions have yet to change. A forward contract's value may become negative or positive, depending on price fluctuations of the underlying asset.

The forward price accounts for various factors. It considers the associated opportunity costs, interest or foregone interest, and any other costs related to the underlying asset and the current spot price. Due to unpredictable market conditions, a forward contract may appreciate or depreciate for both the seller and the purchaser.

Summary

• Forward price refers to the predetermined and agreed upon price of an underlying asset in a forward contract.
• A forward contract refers to an agreement between parties to buy or sell an underlying asset on an agreed-upon date and price.
• The forward price accounts for various factors. It considers the associated opportunity costs, interest or foregone interest, and any other costs related to the underlying asset and the current spot price.

Forward Price Formula

The forward price formula (which assumes zero dividends) is seen below:

F = S₀ x e^rT

Where:

• F = The contract's forward price
• S₀ = The underlying asset's current spot price
• e = The mathematical irrational constant approximated by 2.7183
• r = The risk-free rate that applies to the life of the forward contract
• T = The delivery date in years

Example:

Josh is looking to enter into a forward contract for an investment asset currently trading at $1,000. The risk-free rate in Josh's country is 4%. The forward price for this asset can be calculated as:

F = $1,000 x e^{(0.04 x 1)}

F = $1,040.81

Also, in situations where carrying costs arise, the forward price formula can be expanded to account for the costs, as seen below:

F = S₀ x e^(r+q)T

Where:

• q = Carrying costs

Underlying Assets With Dividends

For a forward contract with which the underlying asset may incur dividends, the forward price is determined with the following formula:

F = (S₀ – D) x e^rT

Where:

• D = The sum of each dividend's present value

Theories that Support the Forward Price Formula

The forward price formula addresses uncertainties around what price a seller of an asset should sell the asset to ensure maximum returns and what price will be suitable for the asset's buyer to maximum returns.

Both parties do not want to incur any losses; hence, they both need to agree upon a fair price. The seller is said to have taken or entered a short position, whereas the buyer is said to have entered a long position. At the very least, we know that both do not want to lose any money in the deal.

An economic variation of the formula will be written as:

Cost of Capital = (Fair Price + Future Value of Asset's Dividends) – Spot Price of Asset

Forward Price = Spot Price – Cost of Carry

To determine the future value of potential dividends of an asset, the risk-free force of interest is used. This is according to the assumption that the situation is risk-free; hence, an investor will be looking to reinvest at the risk-free rate.

The spot price of an underlying asset can be denoted as the market value of the contract at the instant moment of commencement.

More Resources

CFI is the official provider of the Commercial Banking & Credit Analyst (CBCA)™ certification program, designed to transform anyone into a world-class financial analyst.

In order to help you become a world-class financial analyst and advance your career to your fullest potential, these additional resources will be very helpful:

• Forward Contract
• Financial Assets
• Dividend
• Cost of Capital

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Source: https://corporatefinanceinstitute.com/resources/knowledge/trading-investing/forward-price/

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